Question

The function f(x) = –2x2 + 32 represents the height of an object, f(x), after x seconds. How many seconds does it take for the object to hit the ground?

Answer 1

Given:

The height of an object, f(x), after x seconds is

`f(x)=-2x^2+32`

To find:

The time taken be object to hit the ground.

Solution:

We have,

`f(x)=-2x^2+32`

The object will hit the ground if the height is 0, i.e., f(x)=0.

`0=-2x^2+32`

`2x^2=32`

Divide both sides by 2.

`x^2=(32)/(2)`

`x^2=16`

Taking square root on both sides.

`x=\pm 4`

Time cannot be negative. So, x=4.

Therefore, the object will hit the ground after 4 seconds.